JEE Main 2022MathematicsProperties of TrianglesMediumMCQ

JEE Main 2022 — Properties of Triangles Question with Solution

JEE Main 2022 (25 Jun Shift 1)

Question

Let a,b and c be the length of sides of a triangle ABC such that a+b7=b+c8=c+a9. If r and R are the radius of incircle and radius of circumcircle of the triangle ABC, respectively, then the value of Rr is equal to

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Show full solutionCorrect option: C
Correct answer
C52

Step-by-step explanation

Let a+b7=b+c8=c+a9=k

so a+b=7k, b+c=8k, c+a=9k

Solving this we get a=4k, b=3k, c=5k and calculating semi-perimeter 

S=a+b+c2 ⇒S=6k

We know that rR=4sinA2sinB2sinC2

⇒  rR=4s-bs-cbc×s-as-cac×s-as-bab

⇒rR=4·s-as-bs-cabc

⇒rR=4·2k3kk4k3k5k ⇒Rr=52

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About this question

This is a previous-year question from JEE Main 2022, covering the Properties of Triangles chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.